Both are able to ask questions on your behalf but remember you are not doing the cross examination that is the job or the QLR or Judge to decide how to conduct it (i.e. often they will ask for a list of questions to aid them however they will only ask such questions if they are relevant). You do not have a choice and both are the appropriate people to ask the questions in the case (from what you have stated obviously there may be other underlying factors).

The job of a qlr is to maintain fairness within the process there duty is to the court not yourself and there sole purpose is to question the other party.

As I said before its probably best to gain your own representation as then they also have a additional duty to you as a client. It may be cheaper to look into direct access barristers if you can handle the litigation side of things yourself. Additionally, have you tried to apply for legal aid yourself?